Think outside the box. A laptop with a decent external sound card will play CDs, high res, and just about any other format, and outperform just about any conventional CD-only player. I'm using an old iMac ($150 refurbished on EBay) with an Echo Audiofire 2 ($200 street price). 16/44, 24/96, whatever I need.

EDIT: This approach will also allow you to digitize your records in high resolution format for archival purposes at no extra cost.